Saffman-Taylor instabilities in displacements with three immiscible fluids

We investigate the viscous finger instabilities that arise at two interfaces formed by the sequential injection of three Newtonian fluids into a rectangular Hele-Shaw cell. We use linear stability analysis and develop a set of first-order ordinary differential equations to describe the evolution of the perturbations at the interfaces. Based on this approach, we evaluate the problem in a perturbative manner, with emphasis on the analysis of the coupling effect between the two interfaces, quantified by the thickness of the intermediate fluid. Our findings indicate that the interaction between the interfaces is governed by the coupling level between them, influencing both the time required for instability development and the number of viscous fingers formed. Then, we experimentally verified that manipulating the intermediate fluid thickness allows for the delay of instabilities’ development, and that these effects persist in the nonlinear regime. Such findings indicate that the volume of the intermediate phase can be controlled to minimize the deformations of the interfaces and, consequently, increase the efficiency of the displacement process. This phenomenon may be relevant to the industrial sector, serving as a strategy for enhanced oil recovery (EOR) processes, especially those that employ alternate injection of different fluids.